Results 31 to 40 of about 29,416 (289)
Buried points in Julia sets [PDF]
Journal of Difference Equations and Applications, 2010 We give an introduction to buried points in Julia sets and a list of questions about buried points, written to encourage aficionados of topology and dynamics to work on these questions.
Curry, Clinton P., Mayer, John C.
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On the measurable dynamics of real rational functions [PDF]
, 2003 Let f be a real rational function with all critical points on the extended real axis and of even order. Then: (1) f carries no invariant line field on the Julia set unless it is doubly covered by an integral torus endomorphism (a Lattés example); and
Shen, Weixiao, Weixiao Shen
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Limit Directions of Julia Sets of Entire Functions and Complex Differential Equations
Journal of Mathematics, 2023 The limiting directions of Julia sets of infinite order entire functions are studied by combining the theory of complex dynamic system and the theory of complex differential equations, in which the lower bound of the measure of limiting direction of ...
Zhigao Qin, Jianren Long, Xuxu Xiang
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Julia sets as buried Julia components
Transactions of the American Mathematical Society, 2020 Let f f be a rational map with degree
Wang, Youming, Yang, Fei
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Современные информационные технологии и IT-образование, 2023 The proposed article describes the methodology for performing a multi-stage mathematical-informational task "Newton's Method for Complex Polynomials", aimed at developing the creative qualities of students.
Valeriy S. Sekovanov +4 more
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Visualization of Mandelbrot and Julia Sets of Möbius Transformations
Fractal and Fractional, 2021 This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step.
Leah K. Mork, Darin J. Ulness
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Filled Julia Sets of Chebyshev Polynomials [PDF]
, 2021 We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K⊂ C and compare such limits to K.
Christiansen, Jacob Stordal +3 more
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Boundaries of Filled Julia Sets in Generalized Jungck Mann Orbit
IEEE Access, 2019 In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results. We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO.
Dong Li +3 more
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Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
Discrete Dynamics in Nature and Society, 2020 The fractional Potts model on diamond-like hierarchical lattices is introduced in this manuscript, which is a fractional rational system in the complex plane. Then, the fractal dynamics of this model is discussed from the fractal viewpoint.
Weihua Sun, Shutang Liu
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Fractal and Fractional, 2021 In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of ...
Yang Zhao +3 more
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